Lanczos resampling

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Incipit of a piece by Gaspar Sanz. Original, low quality scansion with JPEG artifacts. Open the picture to see the details.
Incipit of a piece by Gaspar Sanz. Original, low quality scansion with JPEG artifacts. Open the picture to see the details.
The same image magnified at 500% with Lanczos algorithm. JPEG artifacts were removed changing image's transfer function. Open the picture to see the details.
The same image magnified at 500% with Lanczos algorithm. JPEG artifacts were removed changing image's transfer function. Open the picture to see the details.

Lanczos resampling is a multivariate interpolation method used to make digital images larger or smaller by resampling them. That is to say, the final values are a weighted sum of the original values (based on relative position to the original image) where the weighting is given by the Lanczos weighted sinc function.

Lanczos uses a windowed product of sinc functions as a convolution kernel for image resampling. In one dimension, its formula is given by: L(x) = \begin{cases} \frac{2 \sin(\pi x) \sin \left( \frac{\pi}{2} x \right)}{\pi^2 x^2} & -2 < x < 2, x \ne 0 \\ 1 & x = 0 \\ 0 & \text{otherwise} \end{cases}.

Lanczos kernel. Note that the function obtains negative values.
Lanczos kernel. Note that the function obtains negative values.

The Lanczos weighted sinc function is theoretically a good image resampling kernel. However, in blind user tests of commonly used resampling kernels, Lanczos was rated below all common bicubic kernels, and just barely above bilinear interpolation.

The filter is named after Cornelius Lanczos, because he showed how to use Fourier series and Chebyshev polynomials for various problems where it was not used before.

The Lanczos resampling kernel is known to be used in:

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